First off, by EFT are you referring to payments on Citicards.com or Pay-by-Phone - if so, if it's after 5pm EST theses payments will post for the next bank business day.
If you're referring to your bank electronically paying Citi (ie. Billpay Service) this is NOT instant.. It can take 3-5 days to post the other creditor (not just Citi).
2nd) in regards to the finance charges, they're called "residual finance charges" Once the payment is LATE or not received in FULL by the due date, it activates a "daily financing" on the account, so finance charges will build up on the account util the balance is paid in full by a duedate, thus far - resulting in 2 month's worth of finance charges, and yes, it includes those new transactions you made.. read your agreement - and no, it's not just Citi.
3rd) Citi advises you in the card agreement, the terms & conditions of the offer, and if you do it by phone, they TELL you "your payments and credits will be allocated to pay off lower rate balances before higher rate balances"